A songbook is a tool I use to get a handle on a song I'm trying to learn. As such, simple is best. Melody line with chord name scribbled above works for me. Also, include at least the first verse and chorus directly under the melody line.
I tried to teach a singer a song from the Christy Moore songbook. He wrote out the melody a the top of each page, then wrote out all the lyrics at the bottom. She had a nasty time keeping track of the phrasing.
If the songs are guitar-based and use funky tunings (DADGAD or CGDGAD), it might be helpful to note the tuning somewhere on the page. If the guitar style is really innovative, a brief guitar lesson could be written as a Foreward.